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Sin x + sin 3x+ sin 5x = 0 |
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Answer» Thanks sinx + sin3x + sin5x = 0»(sinx + sin5x) + sin3x = 0Using the formula sinA + sinB = 2sin(A+B/2)cos(A-B/2) we get»2sin3x*cos2x + sin 3x = 0Taking sin3x common,»sin3x(2cos2x+1) = 0»sin3x = 0 or 2cos2x+1 = 0sin 3x = sin 0 or cos2x = -1/2» 3x = nπ + (-1)^n (0) or cos2x = cos 2π/3» x = nπ/3 or x = (2nπ ± 2π/3)/2» x = nπ/3 or x = nπ ± π/3 |
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